SMAC

This is part of the crystallization module | |

It is only available if you configure PLUMED with ./configure –enable-modules=crystallization . Furthermore, this feature is still being developed so take care when using it and report any problems on the mailing list. |

Calculate a variant on the SMAC collective variable discussed in [50]

The SMAC collective variable can be used to study the formation of molecular solids from either the melt or from solution. The idea behind this variable is that what differentiates a molecular solid from a molecular liquid is an alignment of internal vectors in neighboring molecules. In other words, the relative orientation of neighboring molecules is no longer random as it is in a liquid. In a solid particular torsional angles between molecules are preferred. As such this CV calculates the following average:

\[ s_i = \frac{ \left\{ 1 - \psi\left[ \sum_{j \ne i} \sigma(r_{ij}) \right] \right\} \sum_{j \ne i} \sigma(r_{ij}) \sum_n K_n(\theta_{ij}) }{ \sum_{j \ne i} \sigma(r_{ij}) } \]

In this expression \(r_{ij}\) is the distance between molecule \(i\) and molecule \(j\) and \(\sigma(r_{ij})\) is a switchingfunction that acts on this distance. By including this switching function in the second summation in the numerator and in the denominator we are thus ensuring that we calculate an average over the molecules in the first coordination sphere of molecule \(i\). All molecules in higher coordination sphere will essentially contribute zero to the sums in the above expression because their \(\sigma(r_{ij})\) will be very small. \(\psi\) is also a switching function. The term including \(\psi\) in the numerator is there to ensure that only those molecules that are attached to a reasonably large number of molecules. It is important to include this "more than" switching function when you are simulating nucleation from solution with this CV. Lastly, the $K_n functions are kernelfunctions that take the torsion angle, \(\theta_{ij}\), between the internal orientation vectors for molecules \(i\) and \(j\) as input. These kernel functions should be set so that they are equal to one when the relative orientation of the molecules are as they are in the solid and equal to zero otherwise. The final \(s_i\) quantity thus measures whether (on average) the molecules in the first coordination sphere around molecule \(i\) are oriented as they would be in the solid. Furthermore, this Action is a multicolvar so you can calculate the \(s_i\) values for all the molecules in your system simultaneously and then determine the average, the number less than and so on.

- Examples

In the example below the orientation of the molecules in the system is determined by calculating the vector that connects a pair of atoms. SMAC is then used to determine whether the molecules are sitting in a solid or liquid like environment. We can determine whether the environment is solid or liquid like because in the solid the torsional angle between the bond vectors on adjacent molecules is close to 0 or \(\pi\). The final quantity that is output to the colvar file measures the number of molecules that have a SMAC parameter that is greater than 0.7. N.B. By using the indices of three atoms for each of the MOL keywords below we are telling PLUMED to use the first two numbers to determine the orientation of the molecule that will ultimately be used when calculating the \(\theta_{ij}\) terms in the formula above. The atom with the third index meanwhile is used when we calculate \(r_{ij}\).

Click on the labels of the actions for more information on what each action computes

m3:MOLECULES ...MOL1=9,10,9The numerical indices of the atoms in the molecule.MOL2=89,90,89The numerical indices of the atoms in the molecule.MOL3=473,474,473The numerical indices of the atoms in the molecule.MOL4=1161,1162,1161The numerical indices of the atoms in the molecule.MOL5=1521,1522,1521The numerical indices of the atoms in the molecule.MOL6=1593,1594,1593The numerical indices of the atoms in the molecule.MOL7=1601,1602,1601The numerical indices of the atoms in the molecule.MOL8=2201,2202,2201 ...The numerical indices of the atoms in the molecule.s2:SMAC ...SPECIES=this keyword is used for colvars such as coordination number.m3LOWMEM( default=off ) lower the memory requirementsKERNEL1={GAUSSIAN CENTER=0 SIGMA=0.480}compulsory keywordThe kernels used in the function of the angle You can use multiple instances of this keyword i.e.KERNEL2={GAUSSIAN CENTER=pi SIGMA=0.480}compulsory keywordThe kernels used in the function of the angle You can use multiple instances of this keyword i.e.SWITCH={RATIONAL R_0=0.6}This keyword is used if you want to employ an alternative to the continuous switching function defined above.MORE_THAN={RATIONAL R_0=0.7}calculate the number of variables more than a certain target value.SWITCH_COORD={EXP R_0=4} ... PRINTcompulsory keywordThis keyword is used to define the coordination switching function.ARG=the input for this action is the scalar output from one or more other actions.s2.*FILE=colvarthe name of the file on which to output these quantities

This second example works in a way that is very similar to the previous command. Now, however, the orientation of the molecules is determined by finding the plane that contains the positions of three atoms.

Click on the labels of the actions for more information on what each action computes

m3:PLANES ...MOL1=9,10,11The numerical indices of the atoms in the molecule.MOL2=89,90,91The numerical indices of the atoms in the molecule.MOL3=473,474,475The numerical indices of the atoms in the molecule.MOL4=1161,1162,1163The numerical indices of the atoms in the molecule.MOL5=1521,1522,1523The numerical indices of the atoms in the molecule.MOL6=1593,1594,1595The numerical indices of the atoms in the molecule.MOL7=1601,1602,1603The numerical indices of the atoms in the molecule.MOL8=2201,2202,2203The numerical indices of the atoms in the molecule.VMEAN...calculate the norm of the mean vector.s2:SMAC ...SPECIES=this keyword is used for colvars such as coordination number.m3LOWMEM( default=off ) lower the memory requirementsKERNEL1={GAUSSIAN CENTER=0 SIGMA=0.480}compulsory keywordThe kernels used in the function of the angle You can use multiple instances of this keyword i.e.KERNEL2={GAUSSIAN CENTER=pi SIGMA=0.480}compulsory keywordThe kernels used in the function of the angle You can use multiple instances of this keyword i.e.SWITCH={RATIONAL R_0=0.6}This keyword is used if you want to employ an alternative to the continuous switching function defined above.MORE_THAN={RATIONAL R_0=0.7}calculate the number of variables more than a certain target value.SWITCH_COORD={EXP R_0=3.0} ... PRINTcompulsory keywordThis keyword is used to define the coordination switching function.ARG=the input for this action is the scalar output from one or more other actions.s2.*FILE=colvarthe name of the file on which to output these quantities

- Glossary of keywords and components

- Description of components

When the label of this action is used as the input for a second you are not referring to a scalar quantity as you are in regular collective variables. The label is used to reference the full set of quantities calculated by the action. This is usual when using MultiColvar functions. Generally when doing this the previously calculated multicolvar will be referenced using the DATA keyword rather than ARG.

This Action can be used to calculate the following scalar quantities directly. These quantities are calculated by employing the keywords listed below. These quantities can then be referenced elsewhere in the input file by using this Action's label followed by a dot and the name of the quantity. Some of them can be calculated multiple times with different parameters. In this case the quantities calculated can be referenced elsewhere in the input by using the name of the quantity followed by a numerical identifier e.g. *label*.lessthan-1, *label*.lessthan-2 etc. When doing this and, for clarity we have made it so that the user can set a particular label for each of the components. As such by using the LABEL keyword in the description of the keyword input you can customize the component name

Quantity | Keyword | Description |

between | BETWEEN | the number/fraction of values within a certain range. This is calculated using one of the formula described in the description of the keyword so as to make it continuous. You can calculate this quantity multiple times using different parameters. |

highest | HIGHEST | the highest of the quantities calculated by this action |

lessthan | LESS_THAN | the number of values less than a target value. This is calculated using one of the formula described in the description of the keyword so as to make it continuous. You can calculate this quantity multiple times using different parameters. |

lowest | LOWEST | the lowest of the quantities calculated by this action |

mean | MEAN | the mean value. The output component can be referred to elsewhere in the input file by using the label.mean |

min | MIN | the minimum value. This is calculated using the formula described in the description of the keyword so as to make it continuous. |

moment | MOMENTS | the central moments of the distribution of values. The second moment would be referenced elsewhere in the input file using label.moment-2, the third as label.moment-3, etc. |

morethan | MORE_THAN | the number of values more than a target value. This is calculated using one of the formula described in the description of the keyword so as to make it continuous. You can calculate this quantity multiple times using different parameters. |

- The atoms involved can be specified using

SPECIES | this keyword is used for colvars such as coordination number. In that context it specifies that plumed should calculate one coordination number for each of the atoms specified. Each of these coordination numbers specifies how many of the other specified atoms are within a certain cutoff of the central atom. You can specify the atoms here as another multicolvar action or using a MultiColvarFilter or ActionVolume action. When you do so the quantity is calculated for those atoms specified in the previous multicolvar. This is useful if you would like to calculate the Steinhardt parameter for those atoms that have a coordination number more than four for example |

- Or alternatively by using

SPECIESA | this keyword is used for colvars such as the coordination number. In that context it species that plumed should calculate one coordination number for each of the atoms specified in SPECIESA. Each of these coordination numbers specifies how many of the atoms specifies using SPECIESB is within the specified cutoff. As with the species keyword the input can also be specified using the label of another multicolvar |

SPECIESB | this keyword is used for colvars such as the coordination number. It must appear with SPECIESA. For a full explanation see the documentation for that keyword |

- Compulsory keywords

NN | ( default=6 ) The n parameter of the switching function |

MM | ( default=0 ) The m parameter of the switching function; 0 implies 2*NN |

D_0 | ( default=0.0 ) The d_0 parameter of the switching function |

R_0 | The r_0 parameter of the switching function |

KERNEL | The kernels used in the function of the angle You can use multiple instances of this keyword i.e. KERNEL1, KERNEL2, KERNEL3... |

SWITCH_COORD | This keyword is used to define the coordination switching function. |

- Options

NUMERICAL_DERIVATIVES | ( default=off ) calculate the derivatives for these quantities numerically |

NOPBC | ( default=off ) ignore the periodic boundary conditions when calculating distances |

SERIAL | ( default=off ) do the calculation in serial. Do not use MPI |

LOWMEM | ( default=off ) lower the memory requirements |

TIMINGS | ( default=off ) output information on the timings of the various parts of the calculation |

SWITCH | This keyword is used if you want to employ an alternative to the continuous switching function defined above. The following provides information on the switchingfunction that are available. When this keyword is present you no longer need the NN, MM, D_0 and R_0 keywords. |

MEAN | take the mean of these variables. The final value can be referenced using label.mean. You can use multiple instances of this keyword i.e. MEAN1, MEAN2, MEAN3... The corresponding values are then referenced using label.mean-1, label.mean-2, label.mean-3... |

MORE_THAN | calculate the number of variables more than a certain target value. This quantity is calculated using \(\sum_i 1.0 - \sigma(s_i)\), where \(\sigma(s)\) is a switchingfunction. The final value can be referenced using label.morethan. You can use multiple instances of this keyword i.e. MORE_THAN1, MORE_THAN2, MORE_THAN3... The corresponding values are then referenced using label.morethan-1, label.morethan-2, label.morethan-3... |

LESS_THAN | calculate the number of variables less than a certain target value. This quantity is calculated using \(\sum_i \sigma(s_i)\), where \(\sigma(s)\) is a switchingfunction. The final value can be referenced using label.lessthan. You can use multiple instances of this keyword i.e. LESS_THAN1, LESS_THAN2, LESS_THAN3... The corresponding values are then referenced using label.lessthan-1, label.lessthan-2, label.lessthan-3... |

MIN | calculate the minimum value. To make this quantity continuous the minimum is calculated using \( \textrm{min} = \frac{\beta}{ \log \sum_i \exp\left( \frac{\beta}{s_i} \right) } \) The value of \(\beta\) in this function is specified using (BETA= \(\beta\)) The final value can be referenced using label.min. You can use multiple instances of this keyword i.e. MIN1, MIN2, MIN3... The corresponding values are then referenced using label.min-1, label.min-2, label.min-3... |

BETWEEN | calculate the number of values that are within a certain range. These quantities are calculated using kernel density estimation as described on histogrambead. The final value can be referenced using label.between. You can use multiple instances of this keyword i.e. BETWEEN1, BETWEEN2, BETWEEN3... The corresponding values are then referenced using label.between-1, label.between-2, label.between-3... |

HISTOGRAM | calculate how many of the values fall in each of the bins of a histogram. This shortcut allows you to calculates NBIN quantities like BETWEEN. The final value can be referenced using label.histogram. You can use multiple instances of this keyword i.e. HISTOGRAM1, HISTOGRAM2, HISTOGRAM3... The corresponding values are then referenced using label.histogram-1, label.histogram-2, label.histogram-3... |

MOMENTS | calculate the moments of the distribution of collective variables. The mth moment of a distribution is calculated using \(\frac{1}{N} \sum_{i=1}^N ( s_i - \overline{s} )^m \), where \(\overline{s}\) is the average for the distribution. The moments keyword takes a lists of integers as input or a range. Each integer is a value of \(m\). The final calculated values can be referenced using moment- \(m\). You can use the COMPONENT keyword in this action but the syntax is slightly different. If you would like the second and third moments of the third component you would use MOMENTS={COMPONENT=3 MOMENTS=2-3}. The moments would then be referred to using the labels moment-3-2 and moment-3-3. This syntax is also required if you are using numbered MOMENT keywords i.e. MOMENTS1, MOMENTS2... |

LOWEST | this flag allows you to recover the lowest of these variables. The final value can be referenced using label.lowest |

HIGHEST | this flag allows you to recover the highest of these variables. The final value can be referenced using label.highest |